JoanK - as with everything in the UK, "pudding" is a class-ridden term - I was brought up to call any sweet dish after the main course "pudding", whether it was a hot dish like a pie, crumble, charlotte or rice pudding, or a cold one like ice cream, blancmange (yuk), stewed fruit, etc. In my youth, smart people would have called it "dessert", but now, as the fashions change, "pudding" seems to be the favoured term - there is a lot of pretend "return to the nursery" language in vogue with the young and aspirational. I think many cook books use "pudding" for hot dishes and "dessert" for cold, but my mother would certainly still refer to them all as "pudding".
One thing that we would never ever have called it is "sweet" - I think for my parents it was simply a word that never entered their heads, but for many people that would be a marker of someone trying to be "posh" and failing miserably. I seem to remember that Alison Steadman used it mercilessly in the brilliant "Abigail's Party". For us, sweet refers only to confectionary, as in "sweet shop", "bag of sweets", etc - a sort of generic term for toffees, boiled sweets, mints, even chocolate.
I must find a copy of Nancy Mitford's U & Non-U and see what she has to say about it all.
See how fraught simple conversation can be over here!
Rosemary